When physics helps mathematics: calculation of the sophisticated multiple integral

Details When physics helps mathematics: calculation of the sophisticated multiple integral When physics helps mathematics: calculation of the sophisticated multiple integral

2012-01-10

arxiv.org/abs/1201.1975v1

Mathematics

Classical Analysis and ODEs

13 pages, no figures

Scientific paper

There exists a remarkable connection between the quantum mechanical Landau-Zener problem and purely classical-mechanical problem of a ball rolling on a Cornu spiral. This correspondence allows us to calculate a complicated multiple integral, a kind of multi-dimensional generalization of Fresnel integrals. A direct method of calculation is also considered but found to be successful only in some low-dimensional cases. As a byproduct of this direct method, an interesting new integral representation for $\zeta(2)$ is obtained.

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